I stumbled on this ancient (1997) press release for NASA's SOHO mission-

"The new findings seem to account for a substantial part of the energy needed to cause the very high temperature of the corona, the outermost layer of the Sun's atmosphere. Since the corona's temperature was first measured 55 years ago, scientists have lacked a satisfactory explanation for why that temperature is three million degrees while the visible surface of the Sun is only 11,000 degrees Fahrenheit or about 6,000 degrees Celsius.

It is physically impossible to transfer thermal energy from the cooler surface to the much hotter corona, so the energy transfer had to be in the form of waves or magnetic energy, but no measurement to date had found adequate energy to account for the coronal temperature.

"We now have direct evidence for the upward transfer of magnetic energy from the Sun's surface toward the corona above. There is more than enough energy coming up from the loops of the 'magnetic carpet' to heat the corona to its known temperature," said Dr. Alan Title of the Stanford-Lockheed Institute for Space Research, Lockheed Martin Advanced Technology Center, Palo Alto, CA, who led the research. "Each one of these loops carries as much energy as a large hydroelectric plant, such as the Hoover dam, generates in about a million years!" (snip)

(unsnip)Energy flows from the loops when they interact, producing electrical and magnetic "short circuits." The very strong electric currents in these short circuits are what heats the corona to a temperature of several million degrees. Images from the Extreme ultraviolet Imaging Telescope (EIT) and the Coronal Diagnostics Spectrometer (CDS) on SOHO show the hot gases of the ever-changing corona reacting to the evolving magnetic fields rooted in the solar surface.